Computer Science 455
Instructor: R. P. Burton
Fourth Quiz
Name
_________________________________________ Score
____________/35
1.
Following is a list of methods for implementing rubberbanding
(i.e. drawing a series of rubberband line with one
fixed endpoint and one movable endpoint).
Mark the method that is ineffective.
If all methods are effective, pick the one that is least efficient. If all methods are effective and equally
efficient, pick the one that produces the least desirable results.
a.
repaint the rubberband line with background
whenever the rubberband line is moved
b.
paint the rubberband line using XOR; erase it
by repainting it using XOR
c.
save the contents of each pixel before the rubberband
line is drawn; when the rubberband line is moved,
restore the contents
d.
provide a “bit plane” for the rubberband
lines with priority higher than the frame buffer
e.
re-scanconvert the entire scene every time
the rubberband line is moved
(a)
2.
Strokes intended for on-line character or symbol recognition provide
(pick the most complete answer)
a.
information sufficient to recognize the character or symbol
b.
information sufficient to determine the location of the character or
symbol
c.
(both (a) and (b))
(c)
3.
Suppose an urn of exquisite shape has been made available to have its
surface digitized before it is returned to the
a.
analytic
b.
synthetic
(a)
4.
Suppose you are looking at your monitor attempting to explain 3D
right-handed coordinates and 3D left-handed coordinates to your roommate (or
spouse). Since he/she is a history
major, you are using one of your hands to assist in the explanation. In which case are you less likely to get your
thumb in your eye during the explanation?
Assume X is positive to the right and Y is positive upward.
a.
right-handed coordinates
b.
left-handed coordinates
c.
(both are equally likely to result in a thumb in the eye)
(b)
5.
If you wish to present a single point graphically using parallel axes
coordinates, which of the following best represents the maximum practical
dimensionality of the space in which the point resides?
a.
one
b.
two
c.
three
d.
four
e.
five
f.
ten
(f)
6.
The additional programming required to determine the viewing
coordinates for a stereo presentation is probably ________ the programming
required to determine the viewing coordinates for mono presentation.
a.
minimal if not zero relative to
b.
half again as much as
c.
twice
(a)
7.
Which generally appear to be farther away to more viewers?
a.
thinner lines (with thicker lines appearing closer)
b.
darker lines (with lighter[JAG1] lines appearing closer)
c.
red lines (with blue lines appearing closer)
(b)
8.
Which of the following techniques is least likely to have been drawn
from disciplines which preceded computer graphics chronologically?
a.
projections from 3D to 2D
b.
transformations (translation, scaling, rotation, ...)
c.
visible surface determination
d.
(all are drawn conspicuously from other disciplines)
(c)
9.
Suppose tables exist containing 1) vertex coordinates, 2) edges
described by their vertices, 3) polygons described by their edges, 4) polyhedra described by their polygon surfaces, and 5) hyperpolyhedra described by their polyhedra. During an animation, the hyperpolyhedra
are translated, scaled, rotated, and sheared.
The contents of how many of these tables are altered to reflect (no pun
intended) these changes?
a.
one
b.
two
c.
three
d.
four
e.
all five
(a)
10.
Three vertices (in counter-clockwise order) of a polygon are (0,0,0),
(1,2,3), and (3,2,1). The “A”
coefficient of the plane containing this polygon is _____.
a.
less than 0
b.
0
c.
greater than 0
(a:
0 + 2(1) +2(-3) = -4)
11.
Suppose the equation of a plane is 2x + 3y –4z + 5 = 0, and the eye is
at (6, -7, 8). The eye is _______.
a.
inside the plane
b.
on the plane
c.
outside the plane
(a:
12 – 21 – 32 + 5 = -36)
12.
Suppose matrix M transforms coordinates which represent the vertices of
polygons when the coordinates are premultiplied by
M. What correspondingly transforms the
planar coefficients of these same polygons?
a.
nothing, the coordinates must be transformed and the planar
coefficients computed from the transformed coordinates
b.
M premultiplied
c.
M postmultiplied
d.
M inverse[JAG2]
e.
M transpose
(d)
13.
What do the additional parameters associated with superquadrics
provide?
a.
additional dimensions (beyond 3)
b.
additional flexibility for adjusting shapes
c.
local control of sections of surfaces
d.
higher orders of continuity
(b)
14.
Which of the following would be represented as blobby objects?
a.
your biceps
b.
rubber gloves filled with pumpkin seeds and tied shut at the cuff
c.
a closed, aluminum foil fruit juice bag
d.
(all of the above)
(d)
15.
Which of the following manifests zero-order continuity?
a.
the space between the roof of a car and a window when the window is
partially down
b.
the point where the windshield meets the hood of the car
c.
the point where the right front fender panel meets the right front door
panel
d.
the curved lip of the dorsal fin on the trunk of your car (designed to
keep it from swaying as you drive down the highway)
(b)
16.
All things considered, curves which _______ control points generally
are preferred.
a.
approximate
b.
interpolate
(a)
17.
The convex hull (of a set of Bezier control points, for example) is determined
by ____ of the control points.
a.
none
b.
at least some
c.
all but one
d.
all
(b)
18.
Suppose that you are assigned to produce Bezier curves or B-spline curves (your choice) for 100 separate groups of 5
control points each, and 100 separate sets of 6 control points each. How many total blending functions do you need
to determine? (pick the correct range)
a.
0 to 10
b.
11 to 100
c.
101 to 1000
d.
more than 1000
(b
– 11)
19.
A Bezier curve
a.
always passes through the 0th control point
b.
always passes through the last control point
c.
is always tangent, at the 0th control point, to the line
from the 0th control point to the 1st control point
d.
is always tangent, at the last control point, to the line from the
second-to-last control point to the last control point
e.
(some, but not all of (a) through (d))
f.
(all of (a) through (d))
(f)
20.
What is the degree of the polynomial for a Bezier curve determined by 6
control points?
a.
three
b.
never more than 5
c.
never more than 6
d.
never more than 7
e.
can’t say in general
(b)
21.
Pick the best statement:
a.
B-splines are American Bezier curves, and
that’s the only difference (international patent laws didn’t apply to
mathematical techniques in those days)
b.
B-splines can be defined with more control
points than Bezier curves.
c.
Bezier curves often need to be (or are easier to manage when) pieced
together, but B-splines don’t.
d.
The Bezier mentality applies to curves and surfaces, but the B-spline mentality is limited to curves.
(c)
22.
Which of the following is least likely to be “swept” through
three-dimensional space?
a.
a polygon of more than three vertices
b.
a closed Bezier or B-spline curve
c.
a cube defined by its 6 vertices
d.
(all are reasonable candidates for sweeping)
(c)
23.
Which of the following is least likely to happen to a shape during
sweeping?
a.
translation along a Bezier or B-spline curve
b.
rotation
c.
scaling
d.
reflection
e.
shearing
f.
(all are roughly equally likely to occur)
(d)
24.
Drilling a hole in a block of wood is best characterized as a(n) _____
operation.
a.
union
b.
intersection
c.
difference
d.
complement
(c)
25.
Stereolithography (beams intersecting to
solidify a “goo”) is best characterized as a(n) _____ operation.
a.
union
b.
intersection
c.
difference
d.
complement
(b)
26. The representation of arbitrary, hetergeneous, solid objects can be expected to take ____ the representation of the corresponding polygonal “skins.”
a. less storage space than
b. about the same amount of storage space as
c. half again as much storage space as
d. twice the storage space needed for
e. one, two, or even three orders of magnitude more storage space than
(e)
27. Which of the following generally would not be sufficient to terminate octree subdivision?
a. an octant is void
b. an octant is entirely within a blob of blue goo
c. an octant is entirely filled with blue goo
d. an octant contains a single tetrahedron made of solidified blue goo
e. (all of the above are sufficient to terminate octree subdivision)
(d)
28. How many nonzero entries are in a matrix for translating points in 12-dimensional space?
a. 11
b. 12
c. 13
d. more than 13, but less than 20
e. more than 19, but less than 50
f. more than 49
(e – 25)
29. Rotation “in the principal plane” in 2D requires 2 sines and 2 cosines. Rotation in a “principal plane” in nD requires ____ sines and ____ cosines.
a. 2
b. 3
c. n-1
d. n
e. n+1
(a)
30.
Suppose you wish to derive a rotation transformation matrix for
rotation about an arbitrary axis with endpoints P1 and P2 in three-dimensional
space. A first step could be to place
one of the endpoints at the origin. A
second step could be to rotate about the x-axis to place the arbitrary axis in
the xz-plane.
This rotation about the x-axis requires an awareness of _______ where deltaX is the difference in the x-coordinates of two
endpoints, deltaY is the difference in the
y-coordinates of the two endpoints, and deltaZ is the
difference in the z-coordinates of the two endpoints.
a.
just deltaX
b.
deltaX and deltaY
c.
deltaX and delta Z
d.
delta Y and deltaZ
e.
deltaX, deltaY, and deltaZ
(d)
31.
The most efficient way to do build the ultimate arbitrary rotation
matrix contemplated by the previous problem is to 1) calculate the needed
delta(s), 2) determine a tangent using the delta(s), 3) find an arctangent
using the tangent, 4) and then find the sine and cosine using the angle
determined by the tangent.
a.
true
b.
false
(b)
32.
Continuing the previous problems, how many 4x4 transformation matrices
need to be concatenated to rotate d degrees about the arbitrary axis?
a.
none
b.
4
c.
5
d.
6
e.
7
f.
8
(e)
33.
Continuing the previous problems, how many transformation matrices need
to be concatenated to rotate the transformed data another d degrees, where d
has the same value as in the previous problem?
a.
none
b.
4
c.
5
d.
6
e.
7
f.
8
(a)
34.
When scaling an arbitrary
three-dimensional object, what is the maximum number of points that can
remain fixed in position? Assume the
object is scaled in each dimension by some (non-1) value.
a.
none
b.
1
c.
2
d.
3
(b)
35.
Suppose a European doorknob (i.e. not round) is to be rotated around
its lock cylinder. The doorknob’s
coordinate system is described relative to the door coordinate system which is
described relative to the room coordinate system which happens to be the same
as world coordinates. How many
transformation matrices need to be concatenated to rotate the doorknob 30
degrees? (pick the correct range.)
Assume nothing about the relative orientations of the coordinate
systems.
a.
2 to 5
b.
6 to 9
c.
10 to 13
d.
14 to 17
e.
more than 17
(c
– 13)